Higher-derivative supergravity, wrapped M5-branes, and theories of class R

We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class R. Using results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d correspondence we are able to constrain the two independent coefficients in the four-derivative supergravity Lagrangian. This in turn allows us to calculate the subleading terms in the large- N expansion of supersymmetric partition functions for an infinite class of three-dimensional N = 2 SCFTs of class R. We also determine the leading correction to the Bekenstein-Hawking entropy of asymptotically AdS(4) black holes arising from wrapped M5-branes. In addition, we propose and test some conjectures about the perturbative partition function of Chern-Simons theory with complexified ADE gauge groups on closed hyperbolic three-manifolds.